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$f(x)=ax_{2}+bx+c$

Here, $a,$ $b,$ and $c$ are real numbers with $a =0.$ The term with the highest degree — the quadratic term — is written first. Then, the linear term followed by the constant term are written. The standard form can be used to determine the direction of the parabola, the $y-$intercept, the axis of symmetry, and the vertex.

Direction of the Graph | Opens upward when $a>0$ |
---|---|

Opens downward when $a<0$ | |

$y-$intercept | $c$ |

Axis of Symmetry | $x=-2ab $ |

Vertex | $(-2ab ,f(-2ab ))$ |

$ax_{2}+bx+c=0 $

In this equation, $a$ is not equal to $0.$ The solutions of a quadratic equation written in this form can be found by applying the Quadratic Formula. Both the vertex and the intercept form of a quadratic function can always be written in standard form.

Form | Equation | How to Rewrite? |
---|---|---|

Vertex Form | $y=a(x−h)_{2}+k$ | Expand $(x−h)_{2},$ distribute $a,$ and combine like terms. |

Intercept Form | $y=a(x−p)(x−q)$ | Multiply $a(x−p)(x−q)$ and combine like terms. |